Possible molecular implementations of quantum-dot cellular automata (QCA) with mixed-valence ruthenium complexes are discussed. A study of the geometric and electronic structures of three mixed-valence ruthenium dimers has been done using ab initio Hartree-Fock and hybrid density functional methods at the HF/3-21G and B3LYP/3-21G levels of theory. These complexes are representatives of Robin and Day classes 1, 11, and III. Predicted geometries are compared to experimental data, as well as previous computational studies, where available. The B3LYP method predicts structures in better agreement with experiment than the HF method. The analysis of the orbital energies and localization provides insights into the degree of localization and the Robin-Day classification. They are therefore useful tools for the design of mixed valence compounds for use in molecular QCA.